Improved SPGD algorithm to avoid local extremum for incoherent beam combining

The stochastic parallel gradient descent (SPGD) algorithm and the fast steering mirrors (FSM) are applied for incoherent beam combining in this paper. An equation is derived to calculate the wavefront reflected from the FSM under certain control voltages and the relationship between the strength of random disturbances and the combing efficiency is discussed via simulations, indicating that the combining efficiency is inversely proportional to the square of the strength of disturbance. The maximum value of the acceptable disturbance can be determined though the fitting curve which presents an instructional way to reduce the disturbance in advance. Besides, the SPGD algorithm is improved to overcome the weakness of tending to be trapped in the local extremum in incoherent beam combining. In the proposed algorithm, pattern recognition is used to check whether the algorithm is trapped and an “additional move” can be applied to get out of local extremum. The results of simulations show that the proposed algorithm can improve the performance of the incoherent beam combining. Comparative simulations are conducted where the value of evaluation function is increased about 60% compared to the conventional algorithm under the same conditions. The threshold of disturbance also increases about 15% when the accepted value of evaluation function set to 0.8 in the normalized form showing the feasibility of the method. Also, statistical data shows the proposed method depends less on the gain coefficient.